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Re: st: Not sure how to interpret -somersd- results


From   "Roger B. Newson" <r.newson@imperial.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Not sure how to interpret -somersd- results
Date   Wed, 02 Oct 2013 21:57:51 +0100

Hello Monica

Yes, we can say that 2006 child height z-scores stochastically dominate 1996 child height z-scores, as both 95% confidence limits for Somers' D are above zero.

Your confidence intervals would probably be even better if you used the options

transf(z) tdist

for your -somersd- command, as you would then have asymmetric 95% confidence limits using the t-distribution, instead of symmetric confidence limits using the Normal distribution. These alternative confidence limits would be better, because Somers' D cannot really have a perfectly symmetric sampling distribution when a population association exists, and because I have found, from simulation studies, that the t-distribution gives confidence limits with a coverage probability closer to the advertized level than the Normal distribution. This is probably important if you have only 4 clusters.

I hope this helps. Let me know if you have any more queries.

Best wishes

Roger

Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

Opinions expressed are those of the author, not of the institution.

On 02/10/2013 21:47, Jain, Monica (HarvestPlus) wrote:
I am using -somersd- and I am unsure how to interpret the results to test stochastic dominance. I am using Stata 13 for Windows.

I have a two year cross-section data on heights of children 3-5 years. I want to check if the distribution of heights z-score of children in 2006 first order stochastically dominates those in 1996. From previous threads on stochastic dominance, I saw that one could use Somers D statistic for it. I am using the following command where 2006 is year=1, haz is the height z-score:

        somersd year haz, cluster(district)

and I get the following result:
Somers' D with variable: year
Transformation: Untransformed
Valid observations: 627
Number of clusters: 4

Symmetric 95% CI
                                    (Std. Err. adjusted for 4 clusters in dist)
------------------------------------------------------------------------------
                   |              Jackknife
         year  |      Coef.          Std. Err.        z       P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        haz06 |    .357832   .0434275     8.24   0.000     .2727157    .4429483
-------------+----------------------------------------------------------------

What I know is that the above result indicates that a randomly selected child in 2006 is 36% more likely to have a higher height z-score than a randomly selected child in 1996, than vice versa. But, what I do not know is how do I state this result in terms of stochastic dominance. Can I say that distribution of height z-scores in 2006 first order stochastically dominates the distribution of height z-scores in 1996? Alternatively, can I make any statement about stochastic dominance from the above result? If yes, what would it be?

Monica Jain



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